Question

A model rocket climbs 200 m in 4 seconds. If was moving 10 m/s to begin with what is its final velocity

Answer 1

Answer: 90 m/s

Explanation:

For this situation we will use the following equations:

$y=V_{o}t+\frac{1}{2}at^{2}$ (1)  

$V=V_{o} + at$ (2)  

Where:  

$y=200 m$ is the height of the model rocket at 4 s

$V_{o}=10 m/s$ is the initial velocity of the model rocket

$V$ is the velocity of the rocket at 4 s

$t=4 s$ is the time it takes to the model rocket to reach 200 m

$a$ is the constant acceleration due gravity and the rocket's thrust

Firstly, from equation (1) we have to find $a$:

$200 m=(10 m/s)(4 s)+\frac{1}{2}a(4 s)^{2}$ (3)  

$a=20 m/s^{2}$ (4)  

Now we have to substitute this value of $a$ in (2):

$V=10 m/s + (20 m/s^{2})(4 s)$ (5)  

Finally:

$V=90 m/s$ This is the rocket's final velocity